We present randomized distributed algorithms for the maximal independent set problem (MIS) that, while keeping the time complexity nearly matching the best known, reduce the energy complexity substantially. These algorithms work in the standard CONGEST model of distributed message passing with $O(\log n)$ bit messages. The time complexity measures the number of rounds in the algorithm. The energy complexity measures the number of rounds each node is awake; during other rounds, the node sleeps and cannot perform any computation or communications. Our first algorithm has an energy complexity of $O(\log\log n)$ and a time complexity of $O(\log^2 n)$. Our second algorithm is faster but slightly less energy-efficient: it achieves an energy complexity of $O(\log^2 \log n)$ and a time complexity of $O(\log n \cdot \log\log n \cdot \log^* n)$. Thus, this algorithm nearly matches the $O(\log n)$ time complexity of the state-of-the-art MIS algorithms while significantly reducing their energy complexity from $O(\log n)$ to $O(\log^2 \log n)$.

翻译：我们提出了用于最大独立集问题（MIS）的随机分布式算法，这些算法在将时间复杂度维持在接近已知最优水平的同时，显著降低了能量复杂度。这些算法适用于标准CONGEST模型中的分布式消息传递，每个消息包含$O(\log n)$比特。时间复杂度衡量算法的轮数，而能量复杂度衡量每个节点处于唤醒状态的轮数；在其他轮次中，节点处于休眠状态，无法执行任何计算或通信。我们的第一个算法具有$O(\log\log n)$的能量复杂度和$O(\log^2 n)$的时间复杂度。第二个算法速度更快但能量效率略低：其能量复杂度为$O(\log^2 \log n)$，时间复杂度为$O(\log n \cdot \log\log n \cdot \log^* n)$。因此，该算法几乎与现有最优MIS算法的$O(\log n)$时间复杂度相匹配，同时将其能量复杂度从$O(\log n)$显著降低至$O(\log^2 \log n)$。